st: Multiple Interaction effects after probit

I'm estimating a probit model as depicted below:
Y = F( b1 X1+ b2 X2 + b3 X3 + b13 X1*X3 + b23 X2*X3 + B Z )
X1 X2 and X3 are dummy variables, Z is a matrix of other controls.
I'm interested in these two interaction effects. I know Stata's mfx
command cannot give me correct effects. I'm aware of the inteff
command. But that is designed for only one interaction.
I've read Norton's 2003 Economics Letters paper, and I'm using the
predictnl command to calculate the interaction effects.
Three questions:
1. Does the se option of predictnl give me the standard errors of the
interaction effects?
2. Z matrix includes many (about 50) variables. It's a pain to write
_b[z1]*z1+_b[z2]*z2+...+_b[z50]*z50 when using the predictnl command.
Therefore, I'm first getting the predicted values with predict xb,xb
and then I plug those values into predictnl appropriately. Is this OK?
If not could you recommend a short cut please?
I'm not sure about this because sometimes predictnl gives me very
different standard errors for very close interaction effects. For
example, when calculated interaction effects are 1.200, 1.201 and
1,202, the corresponding standard errors are 0.600, 0.605, 0.601
respectively. I don;t think such jumps are normal.
3. I'm also interested in testing the sum of the interaction effects
is zero. Do you think using wald option of p option of predictnl is
appropriate for that?
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